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scoray [572]
3 years ago
13

Find the next number in the following pattern: 1 5 3 7 5 9 7 ...

Mathematics
1 answer:
daser333 [38]3 years ago
7 0

Answer:  The next number in the given pattern is 11.

Step-by-step explanation:  We are given to find the next number in the following pattern :

1      5     3    7    5    9     7   .   .   .

Let a(n) denotes the n-th number of the give pattern.

Then, we see the following rule if followed by the consecutive terms :

a(1)=1\\\\a(2)=5=1+4=a(1)+4,\\\\a(3)=3=5-2=a(2)-2,\\\\a(4)=7=3+4=a(3)+4,\\\\a(5)=5=7-2=a(4)-2,\\\\a(6)=9=5+4=a(5)+4,\\\\a(7)=7=9-2=a(6)-2,~~~.~~~.~~~.

Therefore, the next term will be the sum of the 7-th number and 4. That is

a(8)=a(7)+4=7+4=11.

Thus, the next number in the given pattern is 11.

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_____

<em>Comment on the triangle</em>

You know the 3-4-5 triangle is a right triangle, because you have seen those numbers many times in relation to the Pythagorean theorem. If you don't know that, then you can check to see by using the Pythagorean theorem:

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